Surface acoustic wave device, surface acoustic wave oscillator, and electronic apparatus

ABSTRACT

A surface acoustic wave device includes: a quartz substrate with Euler angles of (φ, θ, ψ); and an IDT which excites a surface acoustic wave in an upper mode of a stop band; wherein, the Euler angle φ is −60°≦φ≦60°, and the Euler angle φ determines the ranges of the Euler angles θ and ψ.

The entire disclosure of Japanese Patent Application No. 2010-189863,filed Aug. 26, 2010 is expressly incorporated by reference herein.

BACKGROUND

1. Technical Field

The present invention relates to a surface acoustic wave device, asurface acoustic wave oscillator having the surface acoustic wavedevice, and an electronic apparatus, and more particularly, to a surfaceacoustic wave device which has an excellent frequency temperaturecharacteristic, a surface acoustic wave oscillator having the surfaceacoustic wave device, and an electronic apparatus.

2. Related Art

In a surface acoustic wave (SAW) device (such as an SAW resonator),variation in a frequency temperature characteristic is greatly affectedby a stop band of the SAW or a cut angle of a quartz substrate, theshape of an IDT (Interdigital Transducer), and the like.

For example, JP-A-11-214958 discloses a configuration for exciting anupper mode and a lower mode of a stop band of an SAW, a standing wavedistribution in the upper mode and the lower mode of the stop band, andthe like.

JP-A-2006-148622, JP-A-2007-208871, JP-A-2007-267033, andJP-A-2002-100959 disclose that an upper mode of a stop band of an SAWhas a frequency temperature characteristic more excellent than that in alower mode of the stop band. JP-A-2006-148622 and JP-A-2007-208871disclose that a cut angle of a quartz substrate is adjusted and anormalized thickness (H/λ) of an electrode is increased to about 0.1 soas to obtain an excellent frequency temperature characteristic in an SAWdevice using Rayleigh waves.

JP-A-2007-267033 discloses that a cut angle of a quartz substrate isadjusted and a normalized thickness (H/λ) of an electrode is increasedto about 0.045 or greater in an SAW device using Rayleigh waves.

JP-A-2002-100959 discloses that a rotational Y-cut X-propagation quartzsubstrate is employed and that the frequency temperature characteristicis improved, compared with a case where resonance in a lower end of astop band is used, by using resonance in an upper end of the stop band.

In an SAW device employing an ST-cut quartz substrate, grooves aredisposed between electrode fingers of an IDT or between conductor stripsof a reflector, which is disclosed in JP-A-57-5418 and “ManufacturingConditions and Characteristics of Groove-type SAW Resonator”,Technological Research Report of the Institute of Electronics andCommunication Engineers of Japan MW82-59 (1982). The “ManufacturingConditions and Characteristics of Groove type SAW Resonator” alsodiscloses that a frequency temperature characteristic varies dependingon the depth of the grooves.

Japanese Patent No. 3851336 discloses that a configuration for setting acurve representing a frequency temperature characteristic to a threedimensional curve is used in an SAW device employing an LST-cut quartzsubstrate and that any substrate with a cut angle having a temperaturecharacteristic represented by a three dimensional curve could not bediscovered in an SAW device employing Rayleigh waves.

As described above, there exist a variety of factors for improving thefrequency temperature characteristic. Particularly, in the SAW deviceemploying the Rayleigh waves, increase in the thickness of an electrodewhich forms an IDT is considered as one of factors contributing to thefrequency temperature characteristic. However, the present inventorexperimentally found out that an environment resistance characteristicsuch as a temporal variation characteristic or a temperature impactresistance characteristic is deteriorated by increasing the thickness ofthe electrode. Further, in a case where improvement in the frequencytemperature characteristic is a main purpose, the thickness of theelectrode should be increased as described above, and it is thusdifficult to avoid the deterioration in the temporal variationcharacteristic, the temperature impact resistance characteristic or thelike. This is true of a Q value, and thus, it is difficult to increasethe Q value without increasing the thickness of the electrode.

SUMMARY

An advantage of some aspects of the invention is that it provides asurface acoustic wave device, a surface acoustic wave oscillator and anelectronic apparatus which can realize an excellent frequencytemperature characteristic.

APPLICATION EXAMPLE 1

This application example of the invention is directed to a surfaceacoustic wave device including an IDT which is disposed on a main planeof any one of a first quartz substrate with Euler angles of (−60°≦φ≦60°,1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.1803×10²≦θ≦1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.4303×10²,2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|4.2235×10≦ψ≦2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.9905×10),a second quartz substrate with Euler angles of (−60°≦φ≦60°,6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.1700≦θ≦6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.4200,2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.3504×10²≦ψ≦2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.427×10²),and a third quartz substrate with Euler angles of (−60°≦φ≦60°,−2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻⁴×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10⁻¹×|φ|+3.2000×10≦θ≦−2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻⁴×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10⁻¹×|φ|+5.7000×10,−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+8.9090×10≦ψ≦−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+9.6760×10),and which excites a surface acoustic wave in an upper mode of a stopband.

According to the surface acoustic wave resonator with thisconfiguration, it is possible to achieve an excellent frequencytemperature characteristic.

APPLICATION EXAMPLE 2

This application example of the invention is directed to the surfaceacoustic wave device according to Application Example 1, wherein aninter-electrode-finger groove is formed by recessing the substratedisposed between electrode fingers which form the IDT.

By forming the inter-electrode-finger groove, it is possible to suppressthe thickness of the electrode film from being increased. Thus, it ispossible to suppress the characteristic deterioration caused by thematerial which forms the electrode.

APPLICATION EXAMPLE 3

This application example of the invention is directed to the surfaceacoustic wave device according to Application Example 1 or 2, whereinwhen one of the first, second and third quartz substrates is used, aline occupancy η of the IDT satisfies the following expression:0.49≦η≦0.70.

According to the surface acoustic wave device with this configuration,it is possible to maintain a secondary temperature coefficient β, whichis a secondary coefficient in an approximate polynomial expression of acurve which indicates the frequency temperature characteristic of thesurface acoustic wave device, in the range of β=±0.010 ppm/° C.².

APPLICATION EXAMPLE 4

This application example of the invention is directed to the surfaceacoustic wave device according to any one of Application Examples 1 to3, wherein where the depth of the inter-electrode-finger groove is G, Gsatisfies the following expression:0.02λ≦G≦0.04λ.

When at least the depth G is in this range, it is possible to maintainthe secondary temperature coefficient β in the range of β=±0.010 ppm/°C.².

APPLICATION EXAMPLE 5

This application example of the invention is directed to a surfaceacoustic waver oscillator which includes the surface acoustic wavedevice according to any one of Application Examples 1 to 4.

APPLICATION EXAMPLE 6

This application example of the invention is directed to an electronicapparatus which includes the surface acoustic wave device according toany one of Application Examples 1 to 4.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIGS. 1A, 1B, and 1C are diagrams illustrating a configuration of an SAWdevice according to an embodiment of the invention.

FIG. 2 shows a graph for determining Euler angles of a first quartzsubstrate, in which values of θ and ψ are plotted in which a secondarytemperature coefficient is in the range of ±0.010 ppm/° C.², in therelationship with a first rotational angle φ.

FIG. 3 shows a graph illustrating the relationship between an upper modeof a stop band and a lower mode thereof.

FIG. 4 shows a graph illustrating a frequency temperature characteristicin an SAW device when an electrode film thickness H is 0.06λ, a lineoccupancy η is 0.49, and Euler angles are (20°, 134°, 51.2°).

FIG. 5 shows a graph in which values of θ and ψ are plotted in which asecondary temperature coefficient is in the range of ±0.010 ppm/° C.²,in the relationship with a first rotational angle φ, when grooves areformed in the first quartz substrate.

FIG. 6 shows a graph illustrating a frequency temperature characteristicin an SAW device when an electrode film thickness H is 0.02λ, a groovedepth G is 0.04λ, a line occupancy η is 0.42, and Euler angles are (30°,137°, 55.9°).

FIG. 7 is a graph illustrating the relationship between the depth of aninter-electrode-finger groove and a frequency variation in an operatingtemperature range.

FIGS. 8A to 8D are graphs illustrating a difference in a secondarytemperature coefficient due to a variation in a line occupancy η betweena resonance point in the upper mode of the stop band and a resonancepoint in the lower mode of the stop band.

FIG. 9 shows graphs illustrating the relationship between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with an electrode filmthickness of 0.

FIG. 10 shows a graph illustrating the relationship between the depth ofthe inter-electrode-finger groove and the line occupancy η in which thesecondary temperature coefficient is 0 with the electrode film thicknessof 0.

FIG. 11 shows graphs illustrating the relationship between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with an electrode filmthickness of 0.

FIG. 12 is a graph illustrating the relationship between the depth ofthe specific inter-electrode-finger groove when the depth of theinter-electrode-finger groove is deviated by ±0.001λ and a frequencydifference generated in the SAW device according to the deviation.

FIG. 13 shows graphs illustrating the relationship between the depth ofthe inter-electrode-finger groove and the line occupancy η in which thesecondary temperature coefficient is 0 when the electrode film thicknessis changed.

FIG. 14 is a diagram in which the relationships between η1 and the depthof the inter-electrode-finger groove in which the secondary temperaturecoefficient is 0 for each electrode film thickness are arranged in agraph.

FIG. 15 is a diagram in which the relationships between theinter-electrode-finger groove and the line occupancy η are approximatedto straight lines while changing the electrode film thickness from H≈0to H=0.035λ.

FIG. 16 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.01λ.

FIG. 17 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.015λ.

FIG. 18 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.02λ.

FIG. 19 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.025λ.

FIG. 20 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.03λ.

FIG. 21 shows graphs illustrating the relationships between the lineoccupancy η and the secondary temperature coefficient β when the depthof the inter-electrode-finger groove is changed with the electrode filmthickness of 0.035λ.

FIG. 22 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.01λ.

FIG. 23 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.015λ.

FIG. 24 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.02λ.

FIG. 25 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.025λ.

FIG. 26 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.03λ.

FIG. 27 shows graphs illustrating the relationships between the lineoccupancy η and the frequency variation ΔF when the depth of theinter-electrode-finger groove is changed with the electrode filmthickness of 0.035λ.

FIG. 28 shows graphs illustrating the relationships between theinter-electrode-finger groove and the Euler angle ψ when the electrodefilm thickness and the line occupancy η are determined.

FIG. 29 is a diagram in which the relationships between theinter-electrode-finger groove and the Euler angle ψ when the electrodefilm thickness is changed are arranged in a graph.

FIG. 30 is a graph illustrating the relationship between theinter-electrode-finger groove and the Euler angle ψ when the secondarytemperature coefficient β is −0.01 ppm/° C.².

FIG. 31 is a graph illustrating the relationship between theinter-electrode-finger groove and the Euler angle ψ when the secondarytemperature coefficient β is +0.01 ppm/° C.².

FIG. 32 is a graph illustrating the relationship between the Euler angleθ and the secondary temperature coefficient β when the electrode filmthickness is 0.02λ and the depth of the inter-electrode-finger groove is0.04λ.

FIG. 33 is a graph illustrating the relationship between the Euler angleφ and the secondary temperature coefficient β.

FIG. 34 is a graph illustrating the relationship between the Euler angleθ and the Euler angle ψ in which the frequency temperaturecharacteristic is excellent.

FIG. 35 is a diagram illustrating examples of frequency temperaturecharacteristic data in four sample pieces under the condition that thefrequency temperature characteristic is the best.

FIG. 36 is a graph illustrating the relationship between a heightdifference which is the sum of the depth of theinter-electrode-finger-groove and the electrode film thickness and a CIvalue.

FIG. 37 is a table illustrating examples of an equivalent circuitconstant and a static characteristic in the SAW device according to theembodiment of the invention.

FIG. 38 is a diagram illustrating impedance curve data in the SAW deviceaccording to the embodiment of the invention.

FIG. 39 is a graph illustrating the comparison of the relationshipbetween the height difference and the Q value in the SAW deviceaccording to the embodiment of the invention with the relationshipbetween the height difference and the Q value in a related art SAWdevice.

FIG. 40 is a diagram illustrating the SAW reflection characteristic ofthe IDT and the reflector.

FIG. 41 is a graph illustrating the relationship between the electrodefilm thickness and the frequency variation in a heat cycle test.

FIG. 42 shows a graph for determining Euler angles of a second quartzsubstrate, in which values of θ and ψ are plotted in which a secondarytemperature coefficient is in the range of ±0.010 ppm/° C.², in therelationship with a first rotational angle φ.

FIG. 43 shows a graph for determining Euler angles of a third quartzsubstrate, in which values of θ and ψ are plotted in which a secondarytemperature coefficient is in the range of ±0.010 ppm/° C.², in therelationship with a first rotational angle φ.

FIGS. 44A and 44B are diagrams illustrating a configuration of an SAWoscillator according to an embodiment of the invention.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, a surface acoustic wave device, a surface acoustic waveoscillator, and an electronic apparatus according to embodiments of theinvention will be described in detail with reference to the accompanyingdrawings.

Firstly, a surface acoustic wave (SAW) device according to a firstembodiment of the invention will be described with reference to FIGS.1A, 1B, and 1C. FIG. 1A is a plan view of the SAW device, FIG. 1B is apartially enlarged sectional view of the SAW device when a groove isformed between electrode fingers, and FIG. 1C is an enlarged viewillustrating the details of the SAW device in FIG. 1B.

The SAW device 10 according to this embodiment basically includes aquartz substrate 30 and an IDT 12. The SAW device 10 according to thisembodiment is a resonator type in which reflectors 20 are arranged onthe quartz substrate 30. Further, the quartz substrate 30 has crystalaxes which are expressed by an X axis (electrical axis), a Y axis(mechanical axis), and a Z axis (optical axis). For definition of thequartz substrate 30 to be used, an Euler angle display is used. TheEuler angles will be described now. A substrate with the Euler angles of(0°, 0°, 0°) is a Z-cut substrate having a main plane perpendicular tothe Z axis. Here, φ of the Euler angles (φ, θ, ψ) is associated with afirst rotation of the Z-cut substrate, and is a first rotation angle inwhich a rotating direction about the Z axis from the +X axis to the +Yaxis is a positive rotating angle. The Euler angle θ is associated witha second rotation which is carried out after the first rotation of theZ-cut substrate, and is a second rotation angle in which a rotatingdirection about the X axis after the first rotation from the +Y axisafter the first rotation to the +Z axis is a positive rotating angle.The cut plane of a piezoelectric substrate is determined by the firstrotation angle θ and the second rotation angle θ. The Euler angle ψ isassociated with a third rotation which is carried out after the secondrotation of the Z-cut substrate, and is a third rotation angle in whicha rotating direction about the Z axis after the second rotation from the+X axis after the second rotation to the +Y axis after the secondrotation is a positive rotating angle. The propagation direction of theSAW is expressed by the third rotation angle ψ about the X axis afterthe second rotation.

In the related art SAW device, it is known a cut angle in which thefirst rotational angle φ becomes a vicinity of 0° as a point where asecondary temperature coefficient becomes small. In this regard, thepresent applicant experimentally found out that there are three regionswhere the secondary temperature coefficient becomes small when the firstrotational angle φ is changed in the cut angle of the quartz substrate.Further, by simulating ranges where the secondary temperaturecoefficient becomes excellent in the three regions when φ is changed inthe ranges of −60° to +60°, it is possible to obtain graphs as shown inFIGS. 2, 42 and 43, respectively. In FIGS. 2, 42 and 43, upper graphsshows the relationship between the first rotational angle φ and thesecond rotational angle θ, and lower graphs shows the relationshipbetween the first rotational angle φ and the third rotational angle ψ.Further, the ranges where the secondary temperature coefficient becomesexcellent are regions where the secondary temperature coefficient β isin the range of β=±0.010 ppm/° C.². Since the secondary temperaturecoefficient β is a secondary coefficient in an approximate polynomialexpression of a curve indicating a frequency temperature characteristicof an SAW, the fact that an absolute value of the secondary temperaturecoefficient is small means that the variation in the frequency is small,which means that the frequency temperature characteristic is excellent.In FIGS. 2, 42 and 43, the range of φ is set to the range of −60° to+60°, but may have the same repetitive inclination with respect to φ andψ even in the range of φ=±120°, in view of objective properties of aquartz crystalline structure.

In the first embodiment, the SAW device is configured using a firstquartz substrate which is defined in the range of data shown in FIG. 2as the quartz substrate 30. When an approximate curve based on apolynomial expression is obtained on the basis of the plot in FIG. 2,the second rotational angle θ can be expressed as1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.1803×10²≦θ≦1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.4303×10²,in the relationship with the first rotational angle φ. Further, thethird rotational angle ψ can be expressed as2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.2235×10≦ψ≦2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.9905×10,in the relationship with the first rotational angle φ. Accordingly, theEuler angles of the first quartz substrate are determined to be in therange of (−60°≦φ≦60°,1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.1803×10²≦θ≦1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.4303×10²,2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.2235×10≦θ≦2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.9905×10).

The IDT 12 includes a pair of pectinate electrodes 14 a and 14 b inwhich the base end portions of plural electrode fingers 18 are connectedto each other by a bus bar 16. The electrode fingers 18 of one pectinateelectrode 14 a (or 14 b) and the electrode fingers 18 of the otherpectinate electrode 14 b (or 14 a) are alternately arranged with apredetermined gap therebetween. Here, the electrode fingers 18 arearranged in a direction perpendicular to the X′ axis in which thesurface acoustic wave is propagated. The SAW excited by the SAW device10 having the above-mentioned configuration is a Rayleigh type SAW andhas a vibration displacement component in both the Z axis after thethird rotation and the X axis after the third rotation. In this way, bydeviating the propagation direction of the SAW from the X axis which isthe crystal axis of quartz, it is possible to excite the SAW in theupper mode of the stop band.

The SAW in the upper mode of the stop band and the SAW in the lower modeof the stop band will be described now. In the SAWs in the upper modeand the lower mode of the stop band formed by the regular IDT 12 shownin FIG. 3 (where the electrode fingers 18 of the IDT 12 are shown inFIG. 3), the standing waves are deviated in antinode (or node) positionsby π/2 from each other. FIG. 3 is a diagram illustrating a standing wavedistribution in the upper mode and the lower mode of the stop band inthe regular IDT 12.

In FIG. 3, as described above, the standing wave in the lower mode ofthe stop band indicated by a solid line has an antinode at the centerposition of each electrode finger 18, that is, at the reflection centerposition, and the standing wave in the upper mode of the stop bandindicated by a one-dot chained line has a node at the reflection centerposition.

Further, a pair of reflectors 20 is disposed so as to interpose the IDT12 in the propagation direction of the SAW. Specifically, both ends ofplural conductor strips 22 disposed parallel to the electrode fingers 18of the IDT 12 are connected to each other.

An end-reflecting SAW device actively using a reflected wave from an endsurface in the SAW propagation direction of the quartz substrate or amulti-pair IDT-type SAW device exciting a standing wave of an SAW usingonly the IDT by increasing the number of electrode finger pairs of theIDT does not necessarily require the reflector.

In this embodiment, a minimum value of the secondary temperaturecoefficient β is selected, in which an electrode film thickness H whichforms the IDT 12 is 0.06λ (λ is wavelength) and a line occupancy η whichis a ratio between the width of the electrode finger 18 and the widthbetween the electrode fingers is in the range of 0.49≦η≦0.70.

In the SAW device with such a configuration, since the secondarytemperature coefficient β is in the range of β=±0.010 ppm/° C.², it ispossible to achieve an excellent frequency temperature characteristic.For example, the frequency temperature characteristic when the electrodefilm thickness H is 0.06λ, the line occupancy η is 0.49, and the Eulerangles are (20°, 134°, 51.2°) is as shown in a graph in FIG. 4. Thesecondary coefficient (secondary temperature coefficient β) in anapproximate polynomial expression shown in FIG. 4 is 0.0004 ppm/° C.²,which means that the secondary temperature coefficient β becomesremarkably small and thus the frequency temperature characteristic isexcellent.

The electrode films which forms the IDT 12 or the reflectors 20 havingthe above-mentioned configuration may be formed of aluminum (Al) oralloy containing Al as a main component, for example. When the alloy isused as the material of the electrode films, metal other than Al as amain component may be contained at 10% or less in terms of the weight.Further, since the regions where the secondary temperature coefficientbecomes excellent as shown in FIGS. 2, 42 and 43 is related to thecharacteristic of the quartz substrate 30, but is not related to thematerial of the electrode film.

In the quartz substrate 30 of the SAW device 10 having the basicconfiguration described above, grooves (inter-electrode-finger grooves)32 may be formed between the electrode fingers of the IDT 12 or theconductor strips of the reflectors 20. Graphs shown in FIG. 5 illustrateregions of the second rotational angle θ and the third rotational angleψ in which the secondary temperature coefficient β is in the range ofβ=±0.010 ppm/° C.², even when the first rotational angle φ is changed,when the above first quartz substrate is used, the electrode filmthickness H is 0.02λ, the groove depth G is 0.04λ, and η is in the rangeof 0.42≦η≦0.70. It can be seen from FIG. 5 that the excellent frequencytemperature characteristic can be obtained even when the grooves 32 areformed between the electrode fingers. Even when the groove depth G ischanged, the second temperature coefficients β can be respectivelyobtained in the range of β=±0.010 ppm/° C.², as described below.

First Embodiment

H: 0.02λ

G: 0.03λ

Euler angles: (10°, 130°, 47.4°)

β: −0.001

Second Embodiment

H: 0.02λ

G: 0.02λ

Euler angles: (20°, 134°, 53.0°)

β: −0.005

Third Embodiment

H: 0.02λ

G: 0.03λ

Euler angles: (30°, 137°, 56.5°)

β: 0.008

It can be inferred from these results that the excellent frequencytemperature characteristic can be obtained even when the groove depth Gis changed. For example, the frequency temperature characteristic whenthe electrode film thickness H is 0.02λ, the groove depth G is 0.04λ,the line occupancy η is 0.42, and the Euler angles are (30°, 137°,55.9°) is as shown in a graph in FIG. 6. The secondary coefficient(secondary temperature coefficient β) in an approximate polynomialexpression shown in FIG. 6 is 0.0009 ppm/° C.². In this case, anapproximate curve indicating the frequency temperature characteristicbecomes approximately horizontal, which shows that the frequencytemperature characteristic is excellent.

Hereinafter, description will be made to detailed characteristics in astate where the ranges of the Euler angles of the quartz substrate arefurther limited. The limiting condition is that the Euler angles of thefirst quartz substrate are (−1°≦φ≦1°, 117°≦θ≦142°, 41.9°≦|ψ|≦49.57°.When the Euler angles of the quartz substrate 30 are limited as above,the grooves 32 formed between the electrode fingers may have the groovedepth G which satisfies the following expression (1).0.01λ≦G  (1)

When the upper limit of the groove depth G is set, as can be seen fromFIG. 7, it is preferred that the groove depth is set in the range asexpressed by the following expression (2).0.01λ≦G≦0.094λ  (2)

By setting the groove depth G to this range, the frequency variation inthe operating temperature range (−40° C. to +85° C.) can be suppressedto 25 ppm or less as a target value, the details of which will bedescribed later. The groove depth G may be preferably set to satisfy thefollowing expression (3).0.01λ≦G≦0.0695λ  (3)

By setting the groove depth G to this range, the shift quantity of theresonance frequency between the individual SAW devices 10 can besuppressed to a correction range even when a production tolerance occursin the groove depth G.

Further, the line occupancy η is a value obtained by dividing a linewidth L of each electrode finger 18 (the width of a convex portion whena quartz convex portion is formed) by a pitch λ/2 (=L+S) between theelectrode fingers 18, as shown in FIG. 1C. Therefore, the line occupancyη can be expressed by the following expression (4).η=L/(L+S)  (4)

In the SAW device 10 according to this embodiment, the line occupancy ηcan be determined in the range expressed by the following expression(5). As can be seen from the following expression (5), η can be derivedby determining the depth G of the grooves 32.

$\begin{matrix}{{{{- 2.5} \times \frac{G}{\lambda}} + 0.675} \leqq \eta \leqq {{{- 2.5} \times \frac{G}{\lambda}} + 0.775}} & (5)\end{matrix}$

Further, it is preferred that the thickness of the electrode filmmaterial (of the IDT 12, the reflectors 20 or the like) in the SAWdevice 10 according to this embodiment be set in a range of thefollowing expression (6).0<H≦0.035λ  (6)

Further, in consideration of the electrode film thickness expressed byExpression (6), the line occupancy η can be calculated by the followingexpression (7).

$\begin{matrix}{\eta = {{{- 2.533} \times \frac{G}{\lambda}} - {2.269 \times \frac{H}{\lambda}} + 0.785}} & (7)\end{matrix}$

As for the line occupancy η, the production tolerance of the electricalcharacteristic (particularly, the resonance frequency) increases as theelectrode film thickness increases. Accordingly, there is a highpossibility that a production tolerance of ±0.04 or less occurs when theelectrode film thickness H is in the range expressed by the expression(6) and a production tolerance greater than ±0.04 occurs when theelectrode film thickness is in the range of H>0.035λ. However, when theelectrode film thickness H is in the range expressed by the expression(6) and the tolerance of the line occupancy η is ±0.04 or less, it ispossible to embody an SAW device with a small secondary temperaturecoefficient β. That is, the line occupancy η can be extended to therange expressed by the following expression (8) which is obtained byadding the tolerance of ±0.04 to the expression (7).

$\begin{matrix}{\eta = {{{- 2.533} \times \frac{G}{\lambda}} - {2.269 \times \frac{H}{\lambda}} + {0.785 \pm 0.04}}} & (8)\end{matrix}$

In the SAW device 10 according to this embodiment having theabove-mentioned configuration, when the secondary temperaturecoefficient β is within the range of ±0.010 ppm/° C.² and the operatingtemperature range of the SAW is preferably set to −40° C. to +85° C., itis a goal to improve the frequency temperature characteristic until thefrequency variation ΔF in the operating temperature range is 25 ppm orless. Hereinafter, it is proved by simulation that the SAW device havingthe above-mentioned configuration has factors for accomplishing theadvantage of the invention.

In the SAW device whose propagation direction is the direction of thecrystal X axis using a quartz substrate called an ST cut, when theoperating temperature range is constant, the frequency variation ΔF inthe operating temperature range is about 117 ppm and the secondarytemperature coefficient β is about −0.030 ppm/° C.². Further, in the SAWdevice which is formed using an in-plane rotation ST-cut quartzsubstrate in which the cut angle of the quartz substrate and the SAWpropagation direction are expressed by Euler angles (0°, 123°, 45°) andthe operating temperature range is the same, the frequency variation ΔFis about 63 ppm and the secondary temperature coefficient β is about−0.016 ppm/° C.².

As described above, the variation in the frequency temperaturecharacteristic of the SAW device 10 is affected by the line occupancy ηof the electrode fingers 18 or the electrode film thickness H of the IDT12 and the groove depth G. The SAW device 10 according to thisembodiment employs the excitation in the upper mode of the stop band.

FIGS. 8A to 8D are graphs illustrating the variation of the secondarytemperature coefficient β when the line occupancy η is varied and theSAW is propagated by the quartz substrate 30. FIG. 8A shows thesecondary temperature coefficient β in the resonance in the upper modeof the stop band when the groove depth G is 0.02λ, and FIG. 8B shows thesecondary temperature coefficient β in the resonance in the lower modeof the stop band when the groove depth G is 0.02λ. Further, FIG. 8Cshows the secondary temperature coefficient β in the resonance in theupper mode of the stop band when the groove depth G is 0.04λ, and FIG.8D shows the secondary temperature coefficient β in the resonance in thelower mode of the stop band when the groove depth G is 0.04λ. In thesimulation shown in FIGS. 8A to 8D, the SAW is propagated in some way bythe quartz substrate 30 which is not provided with an electrode film soas to reduce the factor varying the frequency temperaturecharacteristic. Further, the Euler angles (0°, 123°, ψ) are used as thecut angle of the quartz substrate 30. A value at which the absolutevalue of the secondary temperature coefficient β is the minimum isproperly selected as ψ.

It can be seen from FIGS. 8A to 8D that the secondary temperaturecoefficient β greatly varies in the vicinity of the line occupancy η of0.6 to 0.7 in the upper mode and the lower mode of the stop band. Bycomparing the variation of the secondary temperature coefficient β inthe lower mode of the stop band with the variation of the secondarytemperature coefficient β in the upper mode of the stop band, it ispossible to conclude the following. That is, when the variation of thesecondary temperature coefficient β in the lower mode of the stop bandis shifted from a minus side to a greater minus side, the characteristicis deteriorated (the absolute value of the secondary temperaturecoefficient β increases). On the other hand, when the variation of thesecondary temperature coefficient β in the upper mode of the stop bandis shifted from the minus side to a plus side, the characteristic isimproved (the absolute value of the secondary temperature coefficient βdecreases).

Accordingly, in order to obtain the excellent frequency temperaturecharacteristic in the SAW device, it is preferable to use the vibrationin the upper mode of the stop band.

The inventor made a study of the relationship between the line occupancyη and the secondary temperature coefficient β when the SAW in the uppermode of the stop band is propagated in the quartz substrate with variousgroove depths G.

FIG. 9 shows simulation graphs illustrating the relationships betweenthe line occupancy η and the secondary temperature coefficient β whenthe groove depth G is varied from 0.01λ (1% λ) to 0.08λ (8% λ). It canbe seen from FIG. 9 that a point with β=0, that is, a point where anapproximate curve representing the frequency temperature characteristicis a cubic curve, starts to appear in the vicinity of the groove depth Gof 0.0125λ (1.25% λ). It can be also seen from FIG. 9 that there are twopoints η with β=0 (a point η1) with β=0 on the side where η is great anda point η2) with β=0 on the side where η is small). It can be also seenfrom FIG. 9 that η2 is greater than η1 in the variation of the lineoccupancy η with respect to the variation of the groove depth G.

This knowledge can be understood more deeply with reference to FIG. 10.FIG. 10 is a graph in which η1 and η2 are plotted in which the secondarytemperature coefficient β is 0 while changing the groove depth G. It canbe seen from FIG. 10 that η1 and η2 decrease as the groove depth Gincreases, but the variation of η2 is great in the vicinity of thegroove depth of G=0.04λ to such an extent that the variation departsfrom the graph expressed in the range of 0.5λ to 0.9λ. That is,variation of the η2 is great with respect to the variation of the groovedepth G.

FIG. 11 shows graphs in which the vertical axis of FIG. 9 is changedfrom the secondary temperature coefficient β to the frequency variationΔF. It can be seen from FIG. 11 that the frequency variation ΔF islowered at two points η1 and η2) with β=0. It can be also seen from FIG.11 that the frequency variation ΔF is suppressed to be small at a pointcorresponding to η1 in any graph with the changed groove depth G out oftwo points with β=0.

According to this tendency, it is preferable for mass products in whichproduction errors can be easily caused that the line occupancy with asmall variation of the point with β=0 relative to the variation of thegroove depth G be employed, that is, that η1 be employed. FIG. 7 shows agraph illustrating the relationship between the frequency variation ΔFat the point η1) in which the secondary temperature coefficient β is theminimum in each groove depth G and the groove depth G. It can be seenfrom FIG. 7 that the lower limit of the groove depth G in which thefrequency variation ΔF is equal to or less than 25 ppm as a target valueis 0.01λ and the groove depth G is equal to or greater than the lowerlimit, that is, the range of the groove depth G is 0.01λ≦G.

In FIG. 7, an example where the groove depth G is equal to or greaterthan 0.08λ in simulation is also shown. In the simulation, the groovedepth G is equal to or greater than 0.01λ, the frequency variation ΔF isequal to or less than 25 ppm, and then the frequency variation ΔFdecreases as the groove depth G increases. However, when the groovedepth G is equal to or greater than 0.09λ, the frequency variation ΔFincreases again. When the groove depth G is greater than 0.094λ, thefrequency variation ΔF becomes greater than 25 ppm.

The graph shown in FIG. 7 is the simulation in a state where theelectrode films such as the IDT 12 and the reflectors 20 are not formedon the quartz substrate 30, but it can be understood that the frequencyvariation ΔF of the SAW device 10 having the electrode films formedthereon is smaller, and the details of which can be seen from FIGS. 20to 25. Accordingly, when the upper limit of the groove depth G isdetermined, the maximum value in a state where the electrode films arenot formed may be set to G≦0.094λ. The range of the groove depth Gsuitable for accomplishing the goal can be expressed by the followingexpression (9).0.01λ≦G≦0.094λ  (9)

The groove depth G in the mass production has a maximum tolerance ofabout ±0.001λ. Accordingly, when the line occupancy η is constant andthe groove depth G is deviated by ±0.001λ, the frequency variation Δf ofeach SAW device 10 is as shown in FIG. 12. It can be seen from FIG. 12that when the groove depth G is deviated by ±0.001λ in G=0.04λ, that is,when the groove depth is in the range of 0.039λ≦G≦0.041λ, the frequencyvariation Δf is about ±500 ppm.

Here, when the frequency variation Δf is less than ±1000 ppm, thefrequency can be adjusted using various means for finely adjusting thefrequency. However, when the frequency variation Δf is equal to orgreater than ±1000 ppm, the static characteristic such as a Q value andCI (Crystal Impedance) value and the long-term reliability are affectedby the frequency adjustment, and thus, the good production rate of theSAW device 10 is deteriorated.

By deriving an approximate expression representing the relationshipbetween the frequency variation Δf [ppm] and the groove depth G from thestraight line connecting the plots shown in FIG. 12, the followingexpression (10) can be obtained.Δf=16334G−137  (10)

Here, the range of G satisfying Δf<1000 ppm is G≦0.0695λ. Accordingly,the range of the groove depth G according to this embodiment ispreferably expressed by the following expression (11).0.01λ≦G≦0.0695λ  (11)

Next, FIG. 13 shows graphs illustrating the relationship between η withthe secondary temperature coefficient of β=0, that is, the lineoccupancy η representing a tertiary temperature characteristic, and thegroove depth G. The quartz substrate 30 has the Euler angles of (0°,123°, ψ). Here, an angle at which the frequency temperaturecharacteristic shows the tendency of the cubic curve, that is, an angleat which the secondary temperature coefficient is β=0, is properlyselected as ψ. The relationships between the Euler angle ψ at which ηwith β=0 is obtained and the groove depth G under the same condition asshown in FIG. 13 are shown in FIG. 28. In the graph with the electrodefilm thickness of H=0.02λ in FIG. 28, the plot of ψ<42° is not shown,but ψ=41.9° at G=0.03λ is shown in the plot of η2 of the graph. The plotof the relationship between the groove depth G at each electrode filmthickness and the line occupancy η is obtained from FIGS. 16 to 21, thedetails of which are described later.

It can be seen from FIG. 13 that the variation of η1 due to thevariation of the groove depth G is smaller than the variation of η2 withany thickness, as described above. Accordingly, η1 is extracted from thegraph of thicknesses in FIG. 13 and is arranged in FIG. 14. It can beseen from FIG. 14 that η1 is concentrated in the line indicated by abroken line. Further, in FIG. 14, the plot indicating the upper limit ofthe line occupancy η represents the SAW device with the electrode filmthickness of H=0.01λ and the plot indicating the lower limit of the lineoccupancy η represents the SAW device with the electrode film thicknessof H=0.035λ. That is, as the electrode film thickness H increases, theline occupancy η in which the secondary temperature coefficient is β=0decreases.

By calculating the approximate expression of the plot indicating theupper limit of the line occupancy η and the plot indicating the lowerlimit of the line occupancy η on the basis of the above description, thefollowing expressions (12) and (13) can be derived.

$\begin{matrix}{\eta = {{{- 2.5} \times \frac{G}{\lambda}} + 0.775}} & (12) \\{\eta = {{{- 2.5} \times \frac{G}{\lambda}} + 0.675}} & (13)\end{matrix}$

It can be understood from the above expressions (12) and (13) that η inthe range surrounded with the broken line in FIG. 14 can be determinedin the range expressed by the following expression (14).

$\begin{matrix}{{{{- 2.5} \times \frac{G}{\lambda}} + 0.675} \leqq \eta \leqq {{{- 2.5} \times \frac{G}{\lambda}} + 0.775}} & (14)\end{matrix}$

Here, when the secondary temperature coefficient β is permitted within±0.01 ppm/° C.², it is confirmed that expressions (11) and (14) are bothsatisfied and thus the secondary temperature coefficient β is in therange of ±0.01 ppm/° C.².

Further, when the relationships between the groove depth G with β=0 andthe line occupancy η in the SAW devices 10 with the electrode filmthickness of H≈0, 0.01λ, 0.02λ, 0.03λ, and 0.035λ are expressed byapproximate straight lines on the basis of the expressions (12) to (14),the straight lines shown in FIG. 15 are obtained. The relationshipsbetween the groove depth G and the line occupancy η in the quartzsubstrate 30 not having an electrode film formed thereon are as shown inFIG. 10.

The relational expression between the groove depth G and the lineoccupancy η in which the frequency temperature characteristic isexcellent can be expressed by the following expression (15) on the basisof the approximate expressions indicating the approximate straight lineswith the electrode thicknesses H.

$\begin{matrix}{\eta = {{{- 2.533} \times \frac{G}{\lambda}} - {2.269 \times \frac{H}{\lambda}} + 0.785}} & (15)\end{matrix}$

As for the line occupancy η, the production tolerance of the electricalcharacteristic (particularly, the resonance frequency) increases as theelectrode film thickness increases. Accordingly, there is a highpossibility that a production tolerance of ±0.04 or less occurs when theelectrode film thickness H is in the range expressed by expression (6)and a production tolerance greater than ±0.04 occurs when the electrodefilm thickness is in the range of H>0.035λ. However, when the electrodefilm thickness H is in the range expressed by the expression (6) and thetolerance of the line occupancy η is ±0.04 or less, it is possible toembody an SAW device with a small secondary temperature coefficient β.That is, when the secondary temperature coefficient β is set to ±0.01ppm/° C.² or less in consideration of the production tolerance of theline occupancy, the line occupancy η can be extended to the rangeexpressed by the following expression (16) which is obtained by addingthe tolerance of ±0.04 to the expression (15).

$\begin{matrix}{\eta = {{{- 2.533} \times \frac{G}{\lambda}} - {2.269 \times \frac{H}{\lambda}} + {0.785 \pm 0.04}}} & (16)\end{matrix}$

FIGS. 16 to 21 show graphs illustrating the relationships between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness is changed to 0.01λ (1% λ), 0.015λ (1.5% λ),0.02λ (2% λ), 0.025λ (2.5% λ), 0.03λ (3% λ), and 0.035λ (3.5% λ) and thegroove depth G is changed.

Further, FIGS. 22 to 27 show graphs illustrating the relationshipsbetween the line occupancy η and the frequency variation ΔF in the SAWdevices 10 corresponding to FIGS. 16 to 21. All the quartz substrateshave the Euler angles of (0°, 123°, ψ) and an angle at which ΔF is theminimum is properly selected for ψ.

Here, FIG. 16 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.01λ and FIG. 22 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.01λ.

Further, FIG. 17 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.015λ and FIG. 23 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.015λ.

Further, FIG. 18 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.02λ and FIG. 24 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.02λ.

Further, FIG. 19 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.025λ and FIG. 25 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.025λ.

Further, FIG. 20 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.03λ and FIG. 26 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.03λ.

Further, FIG. 21 is a diagram illustrating the relationship between theline occupancy η and the secondary temperature coefficient β when theelectrode film thickness H is 0.035λ and FIG. 27 is a diagramillustrating the relationship between the line occupancy η and thefrequency variation ΔF when the electrode film thickness H is 0.035λ.

In the drawings (FIGS. 16 to 27), a minute difference exists in thegraphs, but it can be seen that the variation tendency is similar toFIGS. 9 and 11 which are the graphs illustrating the relationshipsbetween the line occupancy η and the secondary temperature coefficient βand between the line occupancy η and the frequency variation ΔF only inthe quartz substrate 30.

That is, it can be said that the advantage of this embodiment can beobtained in the propagation of the surface acoustic wave only in thequartz substrate 30 excluding the electrode films.

The relationships between ψ acquired from η1 in the graphs shown in FIG.28 and the groove depth G are arranged in FIG. 29. The reason forselecting η1 is as described above. As shown in FIG. 29, even when theelectrode film thickness is changed, it can be seen that the angle of ψis hardly changed and the optimal angle of ψ varies with the variationof the groove depth G. This proves that the variation of the secondarytemperature coefficient β is greatly affected by the shape of the quartzsubstrate 30.

In the same way as described above, the relationships of the groovedepth G to ψ at which the secondary temperature coefficient is β=−0.01ppm/° C.² and ψ at which the secondary temperature coefficient isβ=+0.01 ppm/° C.² are acquired and arranged in FIGS. 30 and 31. When theangle of ψ satisfying −0.01≦β≦+0.01 is calculated from the graphs (FIGS.29 to 31), the angle range of ψ under the above-mentioned condition canbe determined preferably as 43°<ψ<45° and more preferably as43.2°≦ψ≦44.2°.

The variation of the secondary temperature coefficient β when the angleof θ is given, that is, the relationship between θ and the secondarytemperature coefficient β is shown in FIG. 32. Here, the SAW device usedin the simulation includes a quartz substrate in which the cut angle andthe SAW propagation direction are expressed by the Euler angles (0, θ,ψ) and the groove depth G is 0.04λ, where the electrode film thickness His 0.02λ. As for ψ, a value at which the absolute value of the secondarytemperature coefficient β is the minimum is selected in theabove-mentioned angle range on the basis of the set angle of θ. Further,η is set to 0.6383 on the basis of the expression (15).

Under this condition, it can be seen from FIG. 32 illustrating therelationship between θ and the secondary temperature coefficient β thatwhen 0 is in the range of 117° to 142°, the absolute value of thesecondary temperature coefficient β is in the range of 0.01 ppm/° C.².Accordingly, by determining θ in the range of 117°≦θ≦142° with theabove-mentioned set value, it can be said that it is possible toconfigure the SAW device 10 having an excellent frequency temperaturecharacteristic.

FIG. 33 is a graph illustrating the relationship between the angle of φand the secondary temperature coefficient β when the groove depth G is0.04λ, the electrode film thickness H is 0.02λ, and the line occupancy ηis 0.65 in the quartz substrate 30 with the Euler angles of (φ, 123°,43.77°).

It can be seen from FIG. 33 that the secondary temperature coefficient βis lower than −0.01 when φ is −2° and +2°, but the absolute value of thesecondary temperature coefficient β is in the range of 0.01 when φ is inthe range of −1.5° to +1.5°. Accordingly, by determining φ in the rangeof −1.5°≦φ≦+1.5° and preferably −1°≦θ≦+1° with the above-mentioned setvalue, it is possible to configure the SAW device 10 with an excellentfrequency temperature characteristic.

In the above description, the ranges of the optimal values of φ, θ and ψare derived from the relationship to the groove depth G under apredetermined condition. On the other hand, FIG. 34 shows the verydesirable relationship between θ and ψ in which the frequency variationis the minimum in the range of −40° C. to +85° C. and the approximateexpression thereof is calculated. As shown in FIG. 34, the angle of ψvaries with the increase of the angle of θ and increases to draw a cubiccurve. In the example shown in FIG. 34, ψ is 42.79° at θ=117° and ψ is49.57° at θ=142°. The approximate curve of these plots is a curveindicated by a broken line in FIG. 34 and can be expressed by thefollowing expression (17) as an approximate expression.ψ=1.19024×10⁻³×θ³−4.48775×10⁻¹×θ²+5.64362×10¹×θ−2.32327×10³±1.0  (17)

From this expression, ψ can be determined by determining θ and the rangeof ψ when the range of θ is set to the range of 117°≦θ≦142° can be setto 42.79°≦ψ≦49.57°. The groove depth G and the electrode film thicknessH in the simulation are set to G=0.04λ and H=0.02λ, respectively.

For the above-mentioned reason, in this embodiment, by configuring theSAW device 10 under various predetermined conditions, it is possible toobtain an SAW device with an excellent frequency temperaturecharacteristic satisfying a target value.

Further, in the SAW device 10 according to this embodiment, as shown inthe expression (6) and FIGS. 16 to 27, it is possible to improve thefrequency temperature characteristic after the electrode film thicknessH is set to the range of 0<H≦0.035λ. Unlike the improvement of thefrequency temperature characteristic by greatly increasing the thicknessH in the related art, it is possible to improve the frequencytemperature characteristic while maintaining the environment resistancecharacteristic. FIG. 41 shows the relationship between the electrodethickness (Al electrode thickness) and the frequency variation in a heatcycle test. The result of the heat cycle test shown in FIG. 41 isobtained after the cycle in which the SAW device is exposed to anatmosphere of −55° C. for 30 minutes and is then exposed to anatmosphere of +125° C. for 30 minutes is repeated eight times. It can beseen from FIG. 41 that the frequency variation (F variation) in therange of the electrode thickness H of the SAW device 10 according tothis embodiment is equal to or less than ⅓ of that in the case where theelectrode thickness H is 0.06λ and the inter-electrode-finger groove isnot disposed. In any plot of FIG. 41, H+G=0.06λ is set.

A high-temperature shelf test of leaving a sample in an atmosphere of125° C. for 1000 hours was performed on the SAW device produced underthe same condition as shown in FIG. 41. It was confirmed that thefrequency variation before and after the test of the SAW device (underfour conditions of H=0.03λ and G=0.03λ, H=0.02λ and G=0.04λ, H=0.015λand G=0.045λ, and H=0.01λ and G=0.05λ) was equal to or less than ⅓ ofthat of the related art SAW device (under the condition of H=0.06λ andG=0).

In the SAW device 10 produced under the same conditions as describedabove and under the conditions that H+G=0.067λ (with an aluminumthickness of 2000 angstroms and a groove depth of 4700 angstroms), theline occupancy of the IDT is ηi=0.6, the line occupancy of the reflectoris ηr=0.8, the Euler angles are (0°, 123°, 43.5°), the number of IDTpairs is 120, the intersection width is 40λ (λ=10 μm), the number ofreflectors (one side) is 72 (36 pairs), and the tilt angle of theelectrode fingers is zero (the arrangement direction of the electrodefingers is equal to the phase speed direction of the SAW), the frequencytemperature characteristic shown in FIG. 35 is obtained.

FIG. 35 is a graph in which the frequency temperature characteristics offour test samples (n=4) are plotted. It can be seen from FIG. 35 thatthe frequency variation ΔF in the operating temperature range of thetest samples is suppressed to be equal to or less than about 20 ppm.

In this embodiment, the influence on the frequency temperaturecharacteristic depending on the groove depth G and the electrodethickness H has been described. However, the depth (height difference)which is the sum of the groove depth G and the electrode thickness Haffects a static characteristic such as an equivalent circuit constantor CI value or a Q value. For example, FIG. 36 shows a graphillustrating the relationship between the height difference and the CIvalue when the height difference is changed in the range of 0.062λ to0.071λ. It can be seen from FIG. 36 that the CI value converges at theheight difference of 0.067λ and is not changed (not lowered) even at agreater height difference.

The frequency, the equivalent circuit constant, and the staticcharacteristics in the SAW device 10 having the frequency temperaturecharacteristic shown in FIG. 35 are arranged in FIG. 37. Here, Frepresents the frequency, Q represents the Q value, γ represents acapacity ratio, CI represents the CI (Crystal Impedance) value, and Mrepresents a performance index (figure of merit), respectively.

Further, FIG. 39 shows a graph illustrating the comparison of therelationship of the height difference and the Q value in the SAW device10 where the grooves 32 are not formed in the quartz substrate 30 and inthe SAW device 10 where the grooves 32 are formed therein. In FIG. 39,the graph indicated by a thick line represents a characteristic of theSAW device 10 where the grooves 32 are formed, and the graph indicatedby a thin line represents a characteristic of the SAW device 10 wherethe grooves 32 are not formed therein. As can be clearly seen from FIG.39, when the grooves are disposed between the electrode fingers and theresonance in the upper mode of the stop band is used, the Q value in theregion where the height difference (G+H) is equal to or greater than0.0407λ (4.07% λ) is higher than that in the case where the grooves arenot disposed between the electrode fingers and the resonance in thelower mode of the stop band is used.

The basic data of the SAW device in the simulation is as follows. Thebasic data of the SAW device 10 where the grooves are formed includes H:0.02λ, G: variable, IDT line occupancy ηi: 0.6, reflector line occupancyηr: 0.8, Euler angles: (0°, 123°, 43.5°), number of pairs: 120,intersection width W: 40λ (λ=10 μm), number of reflectors (one side):60, and no tilt angle of electrode finger. The basic data of the SAWdevice 10 where the grooves are not formed includes H: variable, G:zero, IDT line occupancy ηi: 0.4, reflector line occupancy ηr: 0.3,Euler angles: (0°, 123°, 43.5°), number of pairs: 120, intersectionwidth W: 40λ (λ=10 μm), number of reflectors (one side): 60, and no tiltangle of electrode finger.

By referring to FIG. 37 or 39 for the purpose of comparison of thecharacteristics of the SAW devices, it can be understood how the SAWdevice 10 according to this embodiment increases in the Q value. It isthought that the increase in the Q value is due to the improvement ofthe energy trapping effect and the reason is as follows.

In order to efficiently trap the energy of the surface acoustic waveexcited in the upper mode of the stop band, the upper end frequency ft2of the stop band of the IDT 12 can be set between the lower endfrequency fr1 of the stop band of the reflector 20 and the upper endfrequency fr2 of the stop band of the reflector 20, as shown in FIG. 40.That is, the frequencies can be set to satisfy the following expression(18).fr1<ft2<fr2  (18)

Accordingly, a reflection coefficient Γ of the reflector 20 becomesgreater at the upper end frequency ft2 of the stop band of the IDT 12and the SAW in the upper mode of the stop band excited from the IDT 12is reflected to the IDT 12 by the reflector 20 with a high reflectioncoefficient. The energy trapping force of the SAW in the upper mode ofthe stop band is strengthened, thereby realizing a resonator with lowloss.

On the other hand, when the relationship among the upper end frequencyft2 of the stop band of the IDT 12, the lower end frequency fr1 of thestop band of the reflector 20, and the upper end frequency fr2 of thestop band of the reflector 20 is set to ft2<fr1 or fr2<ft2, thereflection coefficient Γ of the reflector 20 at the upper end frequencyft2 of the stop band of the IDT 12 becomes small, and thus, it isdifficult to obtain the strong energy trapping.

Here, in order to realize the state expressed by the expression (18), itis necessary to frequency-shift the stop band of the reflector 20 to thehigher band side than the stop band of the IDT 12. Specifically, thisstate can be realized by setting the arrangement pitch of the conductorstrips 22 of the reflector 20 to be smaller than the arrangement pitchof the electrode fingers 18 of the IDT 12. In another method, thethickness of the electrode film formed as the conductor strips 22 of thereflector 20 can be set to be smaller than the thickness of theelectrode film formed as the electrode fingers 18 of the IDT 12 or thedepth of the inter-conductor-strip groove of the reflector 20 can be setto be smaller than the depth of the inter-electrode-finger groove of theIDT 12. A plurality of the methods may be combined.

According to FIG. 37, it is possible to obtain a high figure of merit Min addition to the increase in Q value. FIG. 38 is a graph illustratingthe relationship between the impedance Z and the frequency in the SAWdevice having the characteristics shown in FIG. 37. It can be seen fromFIG. 38 that no useless spurious resonance exists in the vicinity of theresonance point.

In the IDT 12 of the SAW device 10 according to this embodiment, all theelectrode fingers are alternately intersected. However, the SAW device10 according to the invention can exhibit the considerable advantageusing only the quartz substrate. Accordingly, even when the electrodefingers 18 of the IDT 12 are thinned out, the same advantage can beobtained.

Further, the grooves 32 may be disposed partially between the electrodefingers 18 or between the conductor strips 22 of the reflector 20.Particularly, since the center portion of the IDT 12 with a highvibration displacement greatly affects the frequency temperaturecharacteristic, the grooves 32 may be disposed only in the centerportion. With this configuration, it is possible to provide the SAWdevice 10 with an excellent frequency temperature characteristic.

Next, a SAW device according to a second embodiment of the inventionwill be described. The SAW device according to this embodiment isdifferent from the SAW device according to the above-described firstembodiment in that the ranges of the Euler angles on the quartzsubstrate to be used are changed. Specifically, a second quartzsubstrate in which an approximate curve based on a polynomial expressionis calculated on the basis of the plot in FIG. 42 to determine the Eulerangles may be used. The Euler angles of the second quartz anglecalculated as described above may be determined in the range of(−60°≦φ≦60°,6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.1700≦θ≦6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.4200,2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.3504×10²≦ψ≦2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.427×10²).Since the other configuration is the same as that of the SAW deviceaccording to the first embodiment, FIGS. 1A to 1C are used for theentire configuration.

The secondary temperature coefficient value becomes the minimum wherethe electrode film thickness of the IDT for the second quartz substrateexpressed by the Euler angles is 0.06λ, and the line occupancy η is inthe range of 0.49≦η≦0.70. In the SAW device according to this embodimentwith such a configuration, the secondary temperature coefficient β mayalso be in the range of β=±0.010 ppm/° C.². As described above, if thesecondary temperature coefficient β becomes small, it means that thefrequency temperature characteristic becomes excellent. Accordingly, inthe SAW device with the quartz substrate according to this embodiment,it is also possible to achieve an excellent frequency temperaturecharacteristic.

Next, a SAW device according to a third embodiment of the invention willbe described. The SAW device according to this embodiment is differentfrom the SAW devices according to the above-described first and secondembodiments in that the ranges of the Euler angles on the quartzsubstrate to be used are changed. Specifically, a third quartz substratein which an approximate curve based on a polynomial expression iscalculated on the basis of the plot in FIG. 43 to determine the Eulerangles may be used. The Euler angles of the third quartz anglecalculated as described above may be determined in the range of(−60°≦φ≦60°, −2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10×|φ|3.2000×10≦θ≦−2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻⁴×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10⁻¹×|φ|+5.7000×10,−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+8.9090×10≦ψ≦−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+9.6760×10).Since the other configuration is the same as those of the SAW devicesaccording to the first and second embodiments, FIGS. 1A to 1C are usedfor the entire configuration.

The electrode film thickness of the IDT for the third quartz substrateexpressed by the Euler angles is 0.06λ, and the line occupancy η is inthe range of 0.49≦η≦0.70. In the SAW device according to this embodimentwith such a configuration, the secondary temperature coefficient β mayalso be in the range of β=±0.010 ppm/° C.². Accordingly, it is possibleto achieve an excellent frequency temperature characteristic, in asimilar way to the above-mentioned embodiments.

Further, in the above-mentioned embodiment, Al or an alloy containing Alas a main component is used for the electrode films. However, anothermetal may be used for the electrode films as long as it provides thesame advantages as the above-mentioned embodiment.

In the above-mentioned embodiment, the SAW device is simply described,but the SAW filter may be employed as the SAW device according to theinvention. Further, although a one-terminal-pair SAW device having onlyone IDT is exemplified in the above-mentioned embodiment, the inventioncan be applied to a two-terminal-pair SAW device having plural IDTs andcan be also applied to a vertical-coupling or horizontal-couplingdouble-mode SAW filter or multimode SAW filter.

An SAW oscillator according to an embodiment of the invention will bedescribed with reference to FIGS. 44A and 44B. As shown in FIGS. 44A and44B, the SAW oscillator according to this embodiment includes theabove-mentioned SAW device 10, an IC (Integrated Circuit) 50 whichcontrols the driving of the SAW device by applying voltage to the IDT 12of the SAW device 10, and a package which accommodates the elements.FIG. 44A is a plan view in which the lid is excluded and FIG. 44B is asectional view taken along line A-A of FIG. 43A.

In the SAW oscillator 100 according to this embodiment, the SAW device10 and the IC 50 are accommodated in the same package 56, and electrodepatterns 54 a to 54 g formed on a bottom plate 56 a of the package 56,pectinate electrodes 14 a and 14 b of the SAW device 10, and pads 52 ato 52 f of the IC 50 are connected to each other by metal wires 60.Further, a cavity of the package 56 receiving the SAW device 10 and theIC 50 is air-tightly sealed with a lid 58. According to thisconfiguration, the IDT 12 (see FIGS. 1A to 1C), the IC 50, and externalmounting electrodes (not shown) formed on the bottom surface of thepackage 56 can be electrically connected to each other.

Further, the SAW device according to this embodiment of the inventioncan be used as a clock source in a mobile phone or a hard disk, a servercomputer, and a wired or wireless base station. An electronic apparatusaccording to an embodiment of the invention is achieved by mounting theabove-described SAW device on the mobile phone, the hard disk, or thelike.

What is claimed is:
 1. A surface acoustic wave device comprising: an IDTwhich is disposed on a main plane of any one of a first quartz substratewith Euler angles of (−60°≦φ≦60°,1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.1803×10²≦θ≦1.7845×10⁻⁹×|φ|⁶+2.2009×10⁻¹⁷×|φ|⁵−1.1608×10⁻⁵×|φ|⁴−4.6486×10⁻¹³×|φ|³+1.8409×10⁻²×|φ|²−3.1338×10⁻⁹×|φ|+1.4303×10²,2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.2235×10≦ψ≦2.5961×10⁻⁹×|φ|⁶+1.2224×10⁻¹⁷×|φ|⁵−1.6416×10⁻⁵×|φ|⁴−3.2260×10⁻¹³×|φ|³+2.5407×10⁻²×|φ|²−1.2131×10⁻⁹×|φ|+4.9905×10),a second quartz substrate with Euler angles of (−60°≦φ≦60°,6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.1700≦θ≦6.7778×10⁻⁷×|φ|⁶−1.2200×10⁻⁴×|φ|⁵+8.1111×10⁻³×|φ|⁴−2.4133×10⁻¹×|φ|³+3.0521×|φ|²−1.2247×10×|φ|+1.4200,2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.3504×10²≦ψ≦2.7816×10⁻⁹×|φ|⁶+2.7322×10⁻¹⁷×|φ|⁵−1.7524×10⁻⁵×|φ|⁴−1.1334×10⁻¹³×|φ|³+2.7035×10⁻²×|φ|²−9.9045×10⁻¹⁰×|φ|+1.427×10²),and a third quartz substrate with Euler angles of (−60°≦φ≦60°,−2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻⁴×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10⁻¹×|φ|+3.2000×10≦θ≦−2.5000×10⁻⁸×|φ|⁶+4.5000×10⁻⁶×|φ|⁵−3.1667×10⁻⁴×|φ|⁴+1.1000×10⁻²×|φ|³−1.8308×10⁻¹×|φ|²+9.0500×10⁻¹×|φ|+5.7000×10,−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+8.9090×10≦ψ≦−4.3602×10⁻⁹×|φ|⁶−1.2360×10⁻¹⁷×|φ|⁵+2.7151×10⁻⁵×|φ|⁴+3.2536×10⁻¹⁴×|φ|³−4.1462×10⁻²×|φ|²−9.4085×10⁻¹⁰×|φ|+9.6760×10),and which excites a surface acoustic wave in an upper mode of a stopband.
 2. The surface acoustic wave device according to claim 1, whereinan inter-electrode-finger groove is formed by recessing the substratedisposed between electrode fingers which form the IDT.
 3. The surfaceacoustic wave device according to claim 1, wherein when one of thefirst, second and third quartz substrates is used, a line occupancy η ofthe IDT satisfies the following expression:0.49≦η≦0.70.
 4. The surface acoustic wave device according to claim 1,wherein where the depth of the inter-electrode-finger groove is G, Gsatisfies the following expression:0.02λ≦G≦0.04λ.
 5. A surface acoustic wave oscillator comprising thesurface acoustic wave device according to claim
 1. 6. A surface acousticwave oscillator comprising the surface acoustic wave device according toclaim
 2. 7. A surface acoustic wave oscillator comprising the surfaceacoustic wave device according to claim
 3. 8. A surface acoustic waveoscillator comprising the surface acoustic wave device according toclaim
 4. 9. An electronic apparatus comprising the surface acoustic wavedevice according to claim
 1. 10. An electronic apparatus comprising thesurface acoustic wave device according to claim
 2. 11. An electronicapparatus comprising the surface acoustic wave device according to claim3.
 12. An electronic apparatus comprising the surface acoustic wavedevice according to claim 4.